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Establishing a distance between genomes is a significant problem incomputational genomics, because its solution can be used to establishevolutionary relationships including phylogeny.  The "double cut and join" (DCJ) model of chromosomal rearrangement proposedby Yancopoulos et al. has received attention as it can model inversions,translocations, fusion and fission on a multichromosomal genome that maycontain both linear and circular chromosomes. In this paper, we realize the DCJoperator as a group action on the space of multichromosomal genomes. We studythis group action, deriving some properties of the group and findinggroup-theoretic analogues for the key results in the DCJ theory.

Algebraic double cut and join -- A group-theoretic approach to the operator on multichromosomal genomes